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My flat was built in 1983 and it still has the original night storage heaters and water heater. Has the state of the art for electric heating improved since then? Would I benefit from an upgrade?
Yes and yes.
Storage heaters are pretty poor. There are better electric heaters on the market now that will outperform storage heaters.
These could be fitted as like for like replacements but you may have to take the supplies off the timeswitch (eco7) as they would only operate at night.
Other alternatives are things like heatrae sadia electromax boilers which do both hot water with a storage vessel plus the heating. This would be via a wet (radiator) system but heated electrically. The system works well but will cost a bit on installation. Perfect for a flat though with no gas.
From 1983 an upgrade to the insulation and windows may also be more cost effective.
If you can insulate then that's you're best course of action.
1kw of electricity still produces 1kw of heat with these systems - nothing has changed (unless your look at air source heat pumps in which case you could be looking at 3kw of heat from 1 kw of electricity.